Solve for $x$ : $ 7|x + 1| + 8 = -3|x + 1| + 2 $
Explanation: Add $ {3|x + 1|} $ to both sides: $ \begin{eqnarray} 7|x + 1| + 8 &=& -3|x + 1| + 2 \\ \\ { + 3|x + 1|} && { + 3|x + 1|} \\ \\ 10|x + 1| + 8 &=& 2 \end{eqnarray} $ Subtract ${8}$ from both sides: $ \begin{eqnarray} 10|x + 1| + 8 &=& 2 \\ \\ { - 8} &=& { - 8} \\ \\ 10|x + 1| &=& -6 \end{eqnarray} $ Divide both sides by ${10}$ $ \dfrac{10|x + 1|} {{10}} = \dfrac{-6} {{10}} $ Simplify: $ |x + 1| = -\dfrac{3}{5}$ The absolute value cannot be negative. Therefore, there is no solution.